5.6 Modeling Harmonic Motion

A laboratory signal is modeled by $y(t)=4\cos\left(0.6t-1.047197551197\right)$, with time in seconds and output in centimeters. Find amplitude, period, frequency and midline, then sketch one complete cycle and tabulate five quarter-cycle points. Explain whether the coefficient sign changes amplitude or only orientation. Show the derivation, labeled graph and contextual reasoning. Written reasoning and sketches require teacher review; selecting a summary does not verify them. Complete the written work or drawing first. The selected answer checks the result only; your reasoning or drawing needs teacher/self-review.

Amplitude is $|4|=4$, never negative. The midline is $y=0$.
Angular frequency is $\omega=0.6$ radians per second. Thus $P=\dfrac{2\pi }{\omega}=10.471975512$ seconds and $f=\dfrac{1}{P}=0.09549297$ hertz. For very short periods use full precision, not a display rounded to zero.
The argument completes $2\pi$ radians over one cycle. Phase and a negative scale alter the starting position or orientation, not the positive period.

• Use every stated input, sign convention, time origin and unit; derive each requested quantity.
• Draw all requested curves and include all observed points and bounded interval endpoints.
• Accept equivalent exact forms and numerical results within one unit in the last displayed decimal, unless a stricter tolerance is stated. Written proofs, interpretation and sketches require teacher review.